PRP Records

Probable Primes Top 10000

(180278 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
80012^188678-9439556798Lelio R Paula09/2011
800220^43651-850356792Enzo Doria03/2013
80032^188657-237156792Yves Minet10/2013
8004(14^49549+5^49549)/1956789Robert Price05/2013
8005(45^34351-1)/4456788Robert Price05/2014
80067*10^56785-2356786Robert Price04/2016
8007(10^56781-31)/356781Serge Batalov12/2014
80087*10^56779+356780Erik Branger11/2009
800910^56765+25917956766Patrick De Geest09/2013
801010^56765-24949756765Patrick De Geest09/2013
8011t(188706)56764Robert Price04/2015
80122^188551-90432756760Paul Bourdelais11/2012
8013(64*10^56756+17)/956757Robert Price09/2015
8014131101#+14629156757Makoto Morimoto02/2016
80152^188539-11251956756Enzo Doria06/2014
80166^72927+10156749Lelio R Paula10/2012
801720^43617-160356748Enzo Doria03/2013
8018(3^118892-8)/9135892956718Lelio R Paula03/2012
8019(509203*2^188338-1)/356701Lelio R Paula03/2015
802020^43567-562356682Enzo Doria03/2013
80212^188234-11318356665Enzo Doria07/2014
8022(7*2^188215-1)/149731512556651Lelio R Paula01/2014
8023(1017*2^188171-1)/3556647Lelio R Paula03/2015
8024(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
8025(2^188176-1017)/45381454356638Lelio R Paula02/2012
802633*10^56634+756636Robert Price07/2016
8027(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
802814^49413+3356634Lelio R Paula02/2013
80293^118680+11056625Lelio R Paula10/2012
8030(13*10^56624+161)/356625Robert Price04/2017
8031(3^118676-2)/751665326356613Lelio R Paula03/2012
8032(13*2^188062+1)/1756613Lelio R Paula07/2012
80332^188056-131356611Yves Minet08/2012
803420^43510-558356608Enzo Doria03/2013
80352^188032+1228556604Lelio R Paula03/2011
8036(265*10^56588+17)/356590Robert Price05/2016
80372^187959+577556582Lelio R Paula03/2011
8038(5*2^187959+1)/5356581Lelio R Paula07/2012
8039(11*2^187889-1)/35156559Lelio R Paula01/2014
8040(100049^11311+1)/10005056553Faysal YAtim09/2007
8041(19*10^56544-1)/956545Serge Batalov03/2009
804220^43447-892356526Enzo Doria03/2013
80432^187743-11217756517Enzo Doria06/2014
8044(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
80455^80831-2256499Lelio R Paula10/2012
80465^80828-1316656497Enzo Doria02/2013
80477*2^187590-556472Lelio R Paula03/2014
80482^187555+7547356460Enzo Doria04/2016
80492^187541-28356456Yves Minet01/2012
8050(55*10^56453-1)/956454Serge Batalov03/2009
80512^187506-145156445Yves Minet08/2012
80526^72522+14356434Lelio R Paula10/2012
8053(15185*2^187452-1)/94956430Lelio R Paula03/2015
80542^187390+7956411Lelio R Paula03/2011
80552^187386+1290956409Lelio R Paula03/2011
80562^187382+61356408Jason Earls04/2008
8057(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
805820^43337-956383Lelio R Paula02/2013
8059(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
80612^187230+42756362Henri Lifchitz01/2005
806011^54121-948056362Enzo Doria02/2013
8062(21*2^187202-1)/4356354Lelio R Paula01/2014
80632^187173-9156345Lelio R Paula03/2011
8064(23*2^187174-1)/2071988356340Lelio R Paula01/2014
80652^187125-283356331Yves Minet09/2014
80669*7^66655-456331Lelio R Paula09/2014
806718^44874-9756330Lelio R Paula02/2013
806860*79^29679+1956322Serge Batalov03/2016
80695^80571+5656317Lelio R Paula10/2012
80705^80551-2256303Lelio R Paula10/2012
8071(76*10^56281+41)/956282Robert Price10/2015
8072(88*10^56271-43)/956272Robert Price11/2015
8073(5*10^56256-119)/356257Robert Price04/2016
80741508^17691+17691^150856230Serge Batalov05/2014
80753^117844-5856226Lelio R Paula10/2012
807695^28427+256221Lelio R Paula05/2013
80772^186713+7681756207Enzo Doria05/2016
807816534^2505+2505^1653456196Hans Havermann06/2016
807914428^7849+7849^1442856195Hans Havermann06/2016
808014898^5909+5909^1489856189Hans Havermann06/2016
808118^44758+9556184Lelio R Paula02/2013
80822^186555-74156159Lelio R Paula05/2011
8083(4*10^56156+173)/356157Robert Price01/2017
8085(3^117708+7)/44789656156Lelio R Paula03/2012
808415711^3752+3752^1571156156Hans Havermann06/2016
8086(23*2^186549-1)/242902556152Lelio R Paula01/2014
8087387^21694+21694^38756138Norbert Schneider08/2014
80882^186422+1723956119Yves Minet01/2010
80892^186418+424242956118Jason Earls10/2008
8090136^26300+13556113Norbert Schneider04/2015
80915*2^186392+956111Lelio R Paula03/2014
809214345^8152+8152^1434556108Hans Havermann07/2016
8093(5*2^186351-1)/3956097Lelio R Paula01/2014
80942^186319-54123756088Paul Bourdelais11/2012
80952*10^56083-4356084Robert Price07/2017
8096(16*10^56082-61)/956083Serge Batalov05/2009
8097(14*10^56080-143)/356081Robert Price01/2017
8098(265*10^56076+17)/356078Robert Price05/2016
80997^66346-5056069Lelio R Paula10/2012
810020^43094-3356067Lelio R Paula02/2013
810120^43090-138356062Enzo Doria03/2013
81023^117482+266056054Lelio R Paula10/2012
8103(22699*2^186193+1)/11156052Lelio R Paula05/2014
8104(68*10^56042+13)/956043Ray Chandler09/2010
81053*6^71992+5^7199256022Mike Oakes03/2010
810613691^12352+12352^1369156020Hans Havermann07/2016
8107(2^186095+7)/7556019Lelio R Paula02/2012
8108247^23412+23412^24756018Norbert Schneider08/2014
81091839^17156+17156^183956008Serge Batalov05/2014
811013736^11949+11949^1373656007Hans Havermann04/2016
8111(5*2^186036-1)/1156003Lelio R Paula01/2014
8112(299*10^55998-17)/356000Robert Price01/2017
8113p(12103)#/2-12855994Robert Price05/2017
81142^186003-17433755993Gary Barnes09/2009
8116(2^186010+78557)/12355993Lelio R Paula05/2012
811520^43037-9355993Lelio R Paula02/2013
811716375^2626+2626^1637555991Hans Havermann03/2016
811815631^3816+3816^1563155985Hans Havermann03/2016
811921^42335-255977Lelio R Paula08/2013
8120Phi(64736,139)55959Enzo Doria07/2012
812115215^4762+4762^1521555958Hans Havermann03/2016
812219317^788+788^1931755953Anatoly F. Selevich12/2006
812313582^13165+13165^1358255950Hans Havermann08/2016
8124(78557*2^185842+1)/18955947Lelio R Paula06/2014
812515^47562-8655938Lelio R Paula02/2013
81263^117222+455930Lelio R Paula03/2012
812724^40519-23^4051955925Robert Price07/2012
812813636^12623+12623^1363655924Hans Havermann07/2016
81292^185767-9955922Lelio R Paula03/2011
8130(19*2^185750-1)/1555917Lelio R Paula01/2014
813115^47542-5855914Lelio R Paula02/2013
813252211!4+255914Robert Price08/2017
813320^42973-558355910Enzo Doria03/2013
81344*10^55906+2155907Robert Price08/2016
81352^185713-11155906Lelio R Paula03/2011
813613^50174+8855891Lelio R Paula01/2013
813714569^6846+6846^1456955879Hans Havermann08/2016
8138Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
81393^117087-8055865Lelio R Paula10/2012
8140(7*10^55851-43)/955851Robert Price10/2014
81412^185519-16955847Lelio R Paula03/2011
81427^66074+1055840Lelio R Paula10/2012
8143(19*10^55833-49)/355834Robert Price02/2017
8144(2*10^55834-59)/355834Robert Price05/2017
814512^51732+555829Lelio R Paula01/2013
81463*2^185429+755821Lelio R Paula03/2014
8147(9787*2^185420-1)/38155819Lelio R Paula04/2015
814814427^7396+7396^1442755819Hans Havermann08/2016
814910^55811+2155812Robert Price01/2011
815010^55811-7410355811Patrick De Geest12/2012
815111^53591-153055810Enzo Doria11/2012
81522^185355-214555798Lelio R Paula03/2011
815314531^6912+6912^1453155794Hans Havermann07/2016
81542^185327-161555789Lelio R Paula03/2011
81552^185280-1277955775Enzo Doria10/2012
815615504^3955+3955^1550455771Hans Havermann07/2016
8157(2*10^55762-59)/355762Robert Price05/2017
81585^79770-4455757Lelio R Paula10/2012
815918^44416-8555755Lelio R Paula02/2013
81602^185208-45999555754Enzo Doria06/2015
81612^185200+118555751Lelio R Paula03/2011
81627^65964+6^(65964-1)55747Robert Price03/2016
81632^185151-23715755737Gary Barnes09/2009
8164110017^11055-10255734Enzo Doria07/2012
816514754^5987+5987^1475455729Hans Havermann07/2016
816640090!3-955711Robert Price09/2014
81679*10^55707+8955708Robert Price11/2016
81682^185023-225755698Yves Minet06/2009
816918628^977+977^1862855696Anatoly F. Selevich01/2007
81702^185006-9355693Lelio R Paula03/2011
81712^185003-251555692Yves Minet07/2014
81726^71524-1955657Lelio R Paula10/2012
81732^184872-219555653Yves Minet08/2013
8174507^20572+20572^50755648Norbert Schneider06/2016
8175134^26151-13355626Norbert Schneider03/2015
817615340^4221+4221^1534055614Hans Havermann07/2016
817727743!2+255612Robert Price01/2013
817820^42744+8155612Lelio R Paula02/2013
817914609^6406+6406^1460955611Hans Havermann07/2016
81802^184724-11288355608Enzo Doria06/2014
818113507^13074+13074^1350755601Hans Havermann07/2016
81822^184689+12955597Lelio R Paula03/2011
8183(9179*2^184672-1)/19355594Lelio R Paula03/2015
8184(22*10^55592-19)/355593Robert Price02/2017
8185Phi(59984,89)55582Enzo Doria05/2012
818611^53368+1655578Lelio R Paula01/2013
818720^42717-192355577Enzo Doria03/2013
8188117^26870+26870^11755573Serge Batalov05/2014
818912^51488+5555565Lelio R Paula01/2013
8190(44*10^55558-17)/955559Robert Price06/2015
819110^55555+3285755556Patrick De Geest06/2010
819210^55555-13672155555Patrick De Geest06/2010
8193(11*2^184541-1)/35155551Lelio R Paula01/2014
819420^42696-204355549Enzo Doria03/2013
8195(2*10^55544+1)/355544Serge Batalov06/2009
8196(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
81975003^15013-16055537Enzo Doria07/2012
819839^34896-255522Lelio R Paula08/2013
8199(6^71345-61)/555517Lelio R Paula05/2014
82002^184407-301955513Yves Minet10/2014
8201(43*10^55512-61)/955513Robert Price06/2015
820220^42667-84355512Enzo Doria03/2013
8203133^26134-13255505Norbert Schneider03/2015
8204(31*2^184378-1)/71155502Lelio R Paula01/2014
82059*7^65667-455497Lelio R Paula09/2014
82062^184342-17355493Lelio R Paula03/2011
820715^47182+9255491Lelio R Paula02/2013
82085^79378+655483Lelio R Paula10/2012
8209581^20068+20068^58155472Norbert Schneider06/2016
8210(2^184232+1)/25755457Donovan Johnson03/2005
821118^44177-141555455Enzo Doria03/2013
82122^184203-279786755451Enzo Doria04/2016
82132^184189+1755447Lelio R Paula03/2011
82142^184183+2612355445Yves Minet01/2010
8215Phi(77077,10)55441Ray Chandler05/2009
82162^184141-11325155432Enzo Doria07/2014
82172^184093-50461355418Gary Barnes09/2009
8218(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
82192^184044-11126955403Enzo Doria05/2014
822014051^8766+8766^1405155401Hans Havermann07/2016
822198^27819+27819^9855394Serge Batalov05/2014
8222(178*10^55390-7)/955392Robert Price08/2017
822358046^9+9^5804655390Andrey Kulsha02/2004
82247^65536+2*59232-255385Jiahao He07/2017
82252^183980+7524155384Enzo Doria04/2016
822610^55372+3755373Robert Price01/2011
822710^55372-4996755372Patrick De Geest12/2012
8228(13*10^55367+17)/355368Robert Price06/2015
82292*6^71150+755366Lelio R Paula09/2014
823019^43296-6255365Lelio R Paula02/2013
823119^43295+1055364Lelio R Paula02/2013
8232(29*10^55362-11)/955363Robert Price04/2015
8233(37*10^55359+53)/955360Robert Price05/2015
823419^43283+7255349Lelio R Paula02/2013
82352^183800-6555330Lelio R Paula03/2011
823621001^12801-11055329Enzo Doria07/2012
823733^36433-32^3643355325Robert Price04/2012
8238(17*2^183729+1)/14555308Lelio R Paula07/2012
82409^57952+8^(57952-1)55301Robert Price03/2016
823914872^5229+5229^1487255301Hans Havermann08/2016
824161^30972-255296Lelio R Paula08/2013
82422^183671-11253755291Enzo Doria06/2014
8243(2^183687+7)/49793974555287Lelio R Paula02/2012
82443^115873+5655286Lelio R Paula10/2012
824513^49629-8455284Lelio R Paula01/2013
82462^183632-555279Henri Lifchitz08/2005
824713981^8988+8988^1398155277Hans Havermann07/2016
8248(5*2^183585+1)/1355265Lelio R Paula07/2012
82492^183576+17155262Lelio R Paula03/2011
825013^49604+8255257Lelio R Paula01/2013


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!